Reduced stability testing set for a diamond-type family of quasipolynomials

A diamond-type family of quasipolynomials, for which vertex stability results hold, is presented. Both delay independent and delay-dependent stability conditions are given. In the first case, it suffices to check for the stability of a finite testing set of multivariate polynomials. While in the other one, it is also needed to check the stability of several edge sub-families of quasipolynomials.

Domains of PID controller coefficients which guarantee stability and performance for LTI time-delay systems

In this work, the computation of the regions in the space of coefficients of a PID controller, inside which the controller stabilizes an LTI time-delay plant and guarantees a performance specification for the closed-loop system, is addressed. To ascertain the sensor noise attenuation, as a sample performance requirement, the H_∞-norm of the weighted complementary sensitivity function is kept below a desired bound. The problem of minimization of the H_∞-norm is transformed into the simultaneous stabilization of a family of quasipolynomials. Then, the stable domains of the PID coefficients are computed for these quasipolynomials using the parameter space approach. This work extends the previous results on the computation of the stability domains of a PID controller to ensure the desired performance specification for the closed-loop system.